Banach空间中伪压缩映射和增生映射的强收敛定理  

Strong Convergence Theorems for Pseudo Contractive and Accretive Mappings in Banach Spaces

作　　者：荆平 唐艳[1] JING Ping;TANG Yan(Mathematics and Statistics College,Chongqing Technology and Business University,Chongqing 400067,China)

机构地区：[1]重庆工商大学数学与统计学院,重庆400067

出　　处：《河北师范大学学报（自然科学版）》2021年第4期336-343,共8页Journal of Hebei Normal University：Natural Science

基　　金：重庆市自然科学基金(cstc2019jcyj-msxmX0661);重庆市教委科技项目(KJQN201900804);重庆工商大学项目(1952007)。

摘　　要：针对Banach空间中伪压缩算子不动点问题与增生算子零点问题的数值解,提出了一类新的粘性迭代逼近算法.由于连续伪压缩算子比非扩张算子以及严格伪压缩算子的应用意义更为广泛,因此在具有弱序列对偶映射的实Banach空间中,利用伪压缩算子与增生算子的关系,讨论了连续伪压缩算子不动点问题与增生算子变分不等式问题的公共解;利用粘性迭代思想构造了该公共解的数值逼近算法.在适当的条件下,该类算法产生的迭代序列强收敛于连续伪压缩算子不动点问题与增生算子变分不等式问题的某个公共解.该系列强收敛定理推广和统一了相关文献的结论,为非线性算子理论做了补充.A new kind of viscosity iterative approximation algorithm is proposed for solving the fixed point problem of pseudo-contractive operators and the zero point problem of accretive operators in Banach spaces.Since continuous pseudo-contraction operators are more widely applied than nonexpansive operators and strict pseudo-contraction operators,the common solutions of fixed point problems for continuous pseudo-contractive operators and accretive operator variational inequalities are discussed in real Banach spaces with weak sequence dual mappings by using the relationship between pseudo-contraction operators and strictly nonexpansive operators.The numerical approximation algorithm of the common solution is given under the idea of viscosity iteration.The iteration sequence generated by this kind of algorithm converges strongly to a common solution of the fixed point problem for continuous pseudo-contractive operators and the variational inequality problem for accretive operators under appropriate conditions.This series of strong convergence theorems generalize and unify some conclusions of relevant literature,and complement the theory of nonlinear operators.

关 键 词：伪压缩算子 增生算子 变分不等式 粘性逼近 

分 类 号：O177.91[理学—数学]